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The owner of a ranch has 6000 square yards of fencing to enclose grazing land...

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Calculus

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The owner of a ranch has 6000 square yards of fencing to enclose grazing land that is subdivided it into 3 parts by means of fences running parallel to the sides, as diagramed. Let x be the total width and y be the height in the diagram. Find x and y to maximize the amount of land that can be enclosed. a) Label the diagram with x and y- b) Write the function to be maximized (the objective function) in terms of x and y. c) Write the given information as an equation (the constraint equation) in terms of x and y. d) Write the function to be optimized in terms of one variable. e) Find the critical number. f) Show work to verify the critical number corresponds to a minimum. g) How should the rancher build their fences? (Round to nearest foot.) h) What is the maximum area? (Round to nearest dollar.)

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